This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fzonnsub2

Description: If M < N then N - M is a positive integer. (Contributed by Mario Carneiro, 1-Jan-2017)

Ref Expression
Assertion fzonnsub2 
|- ( K e. ( M ..^ N ) -> ( N - M ) e. NN )

Proof

Step Hyp Ref Expression
1 elfzolt3b 
 |-  ( K e. ( M ..^ N ) -> M e. ( M ..^ N ) )
2 fzonnsub 
 |-  ( M e. ( M ..^ N ) -> ( N - M ) e. NN )
3 1 2 syl 
 |-  ( K e. ( M ..^ N ) -> ( N - M ) e. NN )